We all know that in the 2012 election season, outside groups fueled by unlimited checks from wealthy donors have been flooding America’s airwaves with campaign ads. Most of the attention in this sphere has focused on super PACs, the turbocharged offspring of political action committees.

But super PACs have in fact been outspent by another, more secretive type of political organization—nonprofits that declare their primary activity to be advancing “social welfare.” Dozens of so-called social welfare groups—such as the conservative Koch brothers’s Americans for Prosperity, the liberal Priorities USA, and Republican strategist Karl Rove’s Crossroads GPS—have been blanketing swing states with political messages, as the law allows. These organizations do not reveal their donors, and until 60 days before the general election, they were not required even to reveal their expenditures to the Federal Election Commission, as long as their ads do not endorse specific candidates.

None of this is illegal. But some of these social welfare groups do appear to have crossed the legal line. In August, a sweeping investigation by ProPublica found that many of them got formal approval and tax-exempt status from the IRS by misrepresenting their activities. A number of them, in fact, sailed through the IRS approval process by claiming that they would not spend money on influencing elections—only to turn around and purchase political ads as soon as the same day.

Last week, another ProPublica report revealed that a nonprofit was running clearly political ads in the Ohio Senate race—ads that praised the Republican candidate, Josh Mandel, and attacked his Democratic opponent, Sen. Sherrod Brown. That was the Government Integrity Fund, which had pledged to the IRS that it would not spend money on politics.

In the final sprint to the elections, many nonprofits are continuing to pour money into political ads—including some who misrepresented themselves to the IRS. On Tuesday, Politico reported that the nonprofit American Action Network will be launching a multimillion dollar ad campaign in partnership with the super PAC Congressional Leadership Fund on behalf of Republicans in the House of Representatives. This is a group that ProPublica found to have broadly misrepresented its spending in tax returns to minimize its political activity.

Many of these “social welfare” nonprofits properly told the IRS that their activities would be political in nature. But as ProPublica has reported, many social welfare groups got formal recognition by misrepresenting their activities to the IRS. The motive may have been to avoid a slower and more careful IRS approval process.

Who is keeping an eye on this kind of illegality? The media certainly should. And the profusion of nonprofit political ads offers a particularly golden opportunity to do so for reporters in swing states. Testing the accuracy of IRS filings of self-declared social welfare groups that run political ads is a straightforward and easily replicated process. CJR went through it, and also spoke with ProPublica reporters Kim Barker and Justin Elliott, to figure out exactly how its done.

Here’s what we learned. Below are three steps for determining whether a social welfare group is deceiving the public:

1) Identify the sponsor organization

Before anything else, figure out the name of the group that is running the ads. Whether you see a political ad on TV that makes you want to dig into its backers—or you want to search political ads in your local market—you can do so using ProPublica’s Free the Files application. Free the Files scrapes the Federal Communications Commission website each day for the disclosure files that some broadcast stations are required to post when they run political ads. Free the Files can be searched either by television market or by ad buyer.

When you get to the market or organization that you’re looking for—for example, here’s the page for the nonprofit Crossroads GPS—you can click on the ad files shown in the lower left section of the screen to examine specific ad buys. Keep in mind that the overall numbers shown in ProPublica’s application are not totals: they reflect the sum of ad spending that Free the Files volunteers have downloaded, rather than overall spending, and the application only covers several dozen major television markets and not all of the country. For markets not covered in Free the Files, you can go directly to the more cumbersome FCC website, and search by network or affiliate name.

For our story, we decided to examine the group Special OPS OPSEC Education Fund. OPSEC is a group of former special forces officers and CIA officers that has run ads in Virginia markets and on the web accusing President Obama of deliberately leaking national security information for political advantage. PolitiFact has evaluated three of its claims and found them Half True, Mostly False, and False, respectively.

Sasha Chavkin covers political money and influence for CJR's United States Project, our politics and policy desk. He has written for ProPublica, the Center for Public Integrity, and The New York World. Follow him on Twitter @sashachavkin.